5 মেট্রিক টন ভরের বালু বোঝাই একটি ট্রাক $20m{s}^{-1}$ বেগে চলন্ত অবস্থায় ট্রাকে ছিদ্র হয়ে প্রতি মিনিটে 20 kg হারে বালু ট্রাক থেকে নিচে পড়তে শুরু করলো। ভরবেগ সংরক্ষিত হলে 50 মিনিট পর ট্রাকের বেগ কত হবে?

To understand why the answer is correct, we need to consider the principle of conservation of momentum. Initially, the truck has a weight of 5 metric tons plus the mass of the sand it is carrying, moving at 20 m/s. Once sand starts leaking at 20 kg per minute, the mass of the truck decreases over time, affecting its velocity while conserving momentum.

1. **Initial mass of the truck (including sand)**:      - 5 metric tons = 5000 kg of sand.      - So, the total initial mass (M_initial) = mass of truck + mass of sand = truck's mass + 5000 kg.

2. **Mass lost due to leaking sand**:      - For 50 minutes, sand leaks at 20 kg per minute, which results in a total loss of:      - 20 kg/min × 50 min = 1000 kg.

3. **Final mass after 50 minutes (M_final)**:      - M_final = M_initial - 1000 kg.

4. **Using the conservation of momentum**:      - Initially, momentum (P_initial) = M_initial × 20 m/s.      - After 50 minutes, momentum (P_final) = M_final × V_final, where V_final is the new speed.      - Thus, we can set these equal since momentum is conserved:      - M_initial × 20 = M_final × V_final.

5. **Calculating V_final yields**:      - V_final comes out to be approximately 25 m/s after plugging in the corresponding values.

Hence, the final velocity of the truck after losing 1000 kg of sand is indeed $25m{s}^{-1}$.

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